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On the Fedosov Deformation Quantization beyond the Regular Poisson Manifolds

High Energy Physics - Theory 2009-11-07 v1 Quantum Algebra

Abstract

A simple iterative procedure is suggested for the deformation quantization of (irregular) Poisson brackets associated to the classical Yang-Baxter equation. The construction is shown to admit a pure algebraic reformulation giving the Universal Deformation Formula (UDF) for any triangular Lie bialgebra. A simple proof of classification theorem for inequivalent UDF's is given. As an example the explicit quantization formula is presented for the quasi-homogeneous Poisson brackets on two-plane.

Keywords

Cite

@article{arxiv.hep-th/0206039,
  title  = {On the Fedosov Deformation Quantization beyond the Regular Poisson Manifolds},
  author = {V. A. Dolgushev and A. P. Isaev and S. L. Lyakhovich and A. A. Sharapov},
  journal= {arXiv preprint arXiv:hep-th/0206039},
  year   = {2009}
}

Comments

18 pages, no figures

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